Global stability of sirs epidemic models with a class of nonlinear incidence rates and distributed delays

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear incidence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.